#include <deal.II/fe/mapping_fe_field.h>

Detailed Description

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>
class MappingFEField< dim, spacedim, VectorType >::InternalData

Storage for internal data of this mapping. See Mapping::InternalDataBase for an extensive description.

This includes data that is computed once when the object is created (in get_data()) as well as data the class wants to store from between the call to fill_fe_values(), fill_fe_face_values(), or fill_fe_subface_values() until possible later calls from the finite element to functions such as transform(). The latter class of member variables are marked as 'mutable', along with scratch arrays.

Definition at line 290 of file mapping_fe_field.h.

Inheritance diagram for MappingFEField< dim, spacedim, VectorType >::InternalData:

[legend]

Public Member Functions
	InternalData (const FiniteElement< dim, spacedim > &fe, const ComponentMask &mask)
virtual void	reinit (const UpdateFlags update_flags, const Quadrature< dim > &quadrature) override
const double &	shape (const unsigned int qpoint, const unsigned int shape_nr) const
double &	shape (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 1, dim > &	derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 2, dim > &	second_derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 3, dim > &	third_derivative (const unsigned int qpoint, const unsigned int shape_nr)
const Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr) const
Tensor< 4, dim > &	fourth_derivative (const unsigned int qpoint, const unsigned int shape_nr)
virtual std::size_t	memory_consumption () const override

Public Attributes
ObserverPointer< const FiniteElement< dim, spacedim > >	fe
std::vector< double >	shape_values
std::vector< Tensor< 1, dim > >	shape_derivatives
std::vector< Tensor< 2, dim > >	shape_second_derivatives
std::vector< Tensor< 3, dim > >	shape_third_derivatives
std::vector< Tensor< 4, dim > >	shape_fourth_derivatives
std::array< std::vector< Tensor< 1, dim > >, GeometryInfo< dim >::faces_per_cell *(dim - 1)>	unit_tangentials
unsigned int	n_shape_functions
ComponentMask	mask
std::vector< DerivativeForm< 1, dim, spacedim > >	covariant
std::vector< DerivativeForm< 1, dim, spacedim > >	contravariant
std::vector< double >	volume_elements
std::vector< double >	quadrature_weights
std::vector< std::vector< Tensor< 1, spacedim > > >	aux
std::vector< types::global_dof_index >	local_dof_indices
std::vector< double >	local_dof_values
UpdateFlags	update_each

Constructor & Destructor Documentation

◆ InternalData()

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

MappingFEField< dim, spacedim, VectorType >::InternalData::InternalData	(	const FiniteElement< dim, spacedim > &	fe,
		const ComponentMask &	mask )

Constructor.

Member Function Documentation

◆ reinit()

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

virtual void MappingFEField< dim, spacedim, VectorType >::InternalData::reinit	(	const UpdateFlags	update_flags,
		const Quadrature< dim > &	quadrature )

overridevirtual

This function initializes the data fields related to evaluation of the mapping on cells, implemented by (derived) classes. This function is used both when setting up a field of this class for the first time or when a new Quadrature formula should be considered without creating an entirely new object. This is used when the number of evaluation points is different on each cell, e.g. when using FEPointEvaluation for handling particles or with certain non-matching problem settings.

Reimplemented from Mapping< dim, spacedim >::InternalDataBase.

◆ shape() [1/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

const double & MappingFEField< dim, spacedim, VectorType >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr ) const

Shape function at quadrature point. Shape functions are in tensor product order, so vertices must be reordered to obtain transformation.

◆ shape() [2/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

double & MappingFEField< dim, spacedim, VectorType >::InternalData::shape	(	const unsigned int	qpoint,
		const unsigned int	shape_nr )

Shape function at quadrature point. See above.

◆ derivative() [1/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

const Tensor< 1, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr ) const

Gradient of shape function in quadrature point. See above.

◆ derivative() [2/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

Tensor< 1, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr )

Gradient of shape function in quadrature point. See above.

◆ second_derivative() [1/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

const Tensor< 2, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr ) const

Second derivative of shape function in quadrature point. See above.

◆ second_derivative() [2/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

Tensor< 2, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::second_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr )

Second derivative of shape function in quadrature point. See above.

◆ third_derivative() [1/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

const Tensor< 3, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr ) const

Third derivative of shape function in quadrature point. See above.

◆ third_derivative() [2/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

Tensor< 3, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::third_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr )

Fourth derivative of shape function in quadrature point. See above.

◆ fourth_derivative() [1/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

const Tensor< 4, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr ) const

Fourth derivative of shape function in quadrature point. See above.

◆ fourth_derivative() [2/2]

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

Tensor< 4, dim > & MappingFEField< dim, spacedim, VectorType >::InternalData::fourth_derivative	(	const unsigned int	qpoint,
		const unsigned int	shape_nr )

Third derivative of shape function in quadrature point. See above.

◆ memory_consumption()

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

virtual std::size_t MappingFEField< dim, spacedim, VectorType >::InternalData::memory_consumption ( ) const

overridevirtual

Return an estimate (in bytes) for the memory consumption of this object.

Reimplemented from Mapping< dim, spacedim >::InternalDataBase.

Member Data Documentation

◆ fe

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

ObserverPointer<const FiniteElement<dim, spacedim> > MappingFEField< dim, spacedim, VectorType >::InternalData::fe

A pointer to the underlying finite element.

Definition at line 377 of file mapping_fe_field.h.

◆ shape_values

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<double> MappingFEField< dim, spacedim, VectorType >::InternalData::shape_values

Values of shape functions. Access by function shape.

Computed once.

Definition at line 384 of file mapping_fe_field.h.

◆ shape_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<Tensor<1, dim> > MappingFEField< dim, spacedim, VectorType >::InternalData::shape_derivatives

Values of shape function derivatives. Access by function derivative.

Computed once.

Definition at line 391 of file mapping_fe_field.h.

◆ shape_second_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<Tensor<2, dim> > MappingFEField< dim, spacedim, VectorType >::InternalData::shape_second_derivatives

Values of shape function second derivatives. Access by function second_derivative.

Computed once.

Definition at line 399 of file mapping_fe_field.h.

◆ shape_third_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<Tensor<3, dim> > MappingFEField< dim, spacedim, VectorType >::InternalData::shape_third_derivatives

Values of shape function third derivatives. Access by function third_derivative.

Computed once.

Definition at line 407 of file mapping_fe_field.h.

◆ shape_fourth_derivatives

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<Tensor<4, dim> > MappingFEField< dim, spacedim, VectorType >::InternalData::shape_fourth_derivatives

Values of shape function fourth derivatives. Access by function fourth_derivative.

Computed once.

Definition at line 415 of file mapping_fe_field.h.

◆ unit_tangentials

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::array<std::vector<Tensor<1, dim> >, GeometryInfo<dim>::faces_per_cell *(dim - 1)> MappingFEField< dim, spacedim, VectorType >::InternalData::unit_tangentials

Unit tangential vectors. Used for the computation of boundary forms and normal vectors.

This array has (dim-1)*GeometryInfo<dim>::faces_per_cell entries. The first GeometryInfo::faces_per_cell contain the vectors in the first tangential direction for each face; the second set of GeometryInfo::faces_per_cell entries contain the vectors in the second tangential direction (only in 3d, since there we have 2 tangential directions per face), etc.

Filled once.

Definition at line 432 of file mapping_fe_field.h.

◆ n_shape_functions

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

unsigned int MappingFEField< dim, spacedim, VectorType >::InternalData::n_shape_functions

Number of shape functions. If this is a Q1 mapping, then it is simply the number of vertices per cell. However, since also derived classes use this class (e.g. the Mapping_Q() class), the number of shape functions may also be different.

Definition at line 440 of file mapping_fe_field.h.

◆ mask

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

ComponentMask MappingFEField< dim, spacedim, VectorType >::InternalData::mask

Stores the mask given at construction time. If no mask was specified at construction time, then a default one is used, which makes this class works in the same way of MappingQEulerian(), i.e., the first spacedim components of the FiniteElement are used for the euler_vector and the euler_dh.

If a mask is specified, then it has to match the underlying FiniteElement, and it has to have exactly spacedim non-zero elements, indicating the components (in order) of the FiniteElement which will be used for the euler vector and the euler dof handler.

Definition at line 454 of file mapping_fe_field.h.

◆ covariant

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<DerivativeForm<1, dim, spacedim> > MappingFEField< dim, spacedim, VectorType >::InternalData::covariant

mutable

Tensors of covariant transformation at each of the quadrature points. The matrix stored is the Jacobian * G^{-1}, where G = Jacobian^{t} * Jacobian, is the first fundamental form of the map; if dim=spacedim then it reduces to the transpose of the inverse of the Jacobian matrix, which itself is stored in the contravariant field of this structure.

Computed on each cell.

Definition at line 465 of file mapping_fe_field.h.

◆ contravariant

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<DerivativeForm<1, dim, spacedim> > MappingFEField< dim, spacedim, VectorType >::InternalData::contravariant

mutable

Tensors of contravariant transformation at each of the quadrature points. The contravariant matrix is the Jacobian of the transformation, i.e. \(J_{ij}=dx_i/d\hat x_j\).

Computed on each cell.

Definition at line 474 of file mapping_fe_field.h.

◆ volume_elements

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<double> MappingFEField< dim, spacedim, VectorType >::InternalData::volume_elements

mutable

The determinant of the Jacobian in each quadrature point. Filled if update_volume_elements.

Definition at line 480 of file mapping_fe_field.h.

◆ quadrature_weights

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<double> MappingFEField< dim, spacedim, VectorType >::InternalData::quadrature_weights

mutable

Projected quadrature weights.

Definition at line 485 of file mapping_fe_field.h.

◆ aux

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<std::vector<Tensor<1, spacedim> > > MappingFEField< dim, spacedim, VectorType >::InternalData::aux

mutable

Auxiliary vectors for internal use.

Definition at line 490 of file mapping_fe_field.h.

◆ local_dof_indices

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<types::global_dof_index> MappingFEField< dim, spacedim, VectorType >::InternalData::local_dof_indices

mutable

Storage for the indices of the local degrees of freedom.

Definition at line 495 of file mapping_fe_field.h.

◆ local_dof_values

template<int dim, int spacedim = dim, typename VectorType = Vector<double>>

std::vector<double> MappingFEField< dim, spacedim, VectorType >::InternalData::local_dof_values

mutable

Storage for local degrees of freedom.

Definition at line 500 of file mapping_fe_field.h.

◆ update_each

template<int dim, int spacedim = dim>

UpdateFlags Mapping< dim, spacedim >::InternalDataBase::update_each

inherited

A set of update flags specifying the kind of information that an implementation of the Mapping interface needs to compute on each cell or face, i.e., in Mapping::fill_fe_values() and friends.

This set of flags is stored here by implementations of Mapping::get_data(), Mapping::get_face_data(), or Mapping::get_subface_data(), and is that subset of the update flags passed to those functions that require re-computation on every cell. (The subset of the flags corresponding to information that can be computed once and for all already at the time of the call to Mapping::get_data() – or an implementation of that interface – need not be stored here because it has already been taken care of.)

Definition at line 704 of file mapping.h.

The documentation for this class was generated from the following file:

include/deal.II/fe/mapping_fe_field.h

Detailed Description

Public Member Functions

Public Attributes

Constructor & Destructor Documentation

◆ InternalData()

Member Function Documentation

◆ reinit()

◆ shape() [1/2]

◆ shape() [2/2]

◆ derivative() [1/2]

◆ derivative() [2/2]

◆ second_derivative() [1/2]

◆ second_derivative() [2/2]

◆ third_derivative() [1/2]

◆ third_derivative() [2/2]

◆ fourth_derivative() [1/2]

◆ fourth_derivative() [2/2]

◆ memory_consumption()

Member Data Documentation

◆ fe

◆ shape_values

◆ shape_derivatives

◆ shape_second_derivatives

◆ shape_third_derivatives

◆ shape_fourth_derivatives

◆ unit_tangentials

◆ n_shape_functions

◆ mask

◆ covariant

◆ contravariant

◆ volume_elements

◆ quadrature_weights

◆ aux

◆ local_dof_indices

◆ local_dof_values

◆ update_each